# Nonlinear electromagnetic fields and symmetries

## TL;DR

This paper generalizes classical symmetry inheritance results for electromagnetic fields to a broader class of nonlinear models, including Born-Infeld and Euler-Heisenberg types, and explores implications for horizons and higher dimensions.

## Contribution

It extends symmetry inheritance theorems to nonlinear electromagnetic models and introduces new constraints for higher-dimensional fields.

## Key findings

- Electromagnetic scalar potentials are constant on Killing horizons.
- Symmetry inheritance is proven for a wide class of nonlinear models.
- New constraints are derived for higher-dimensional electromagnetic fields.

## Abstract

We extend the classical results on the symmetry inheritance of the canonical electromagnetic fields, described by the Maxwell's Lagrangian, to a much wider class of models, which include those of the Born-Infeld, power Maxwell and the Euler-Heisenberg type. Symmetry inheriting fields allow the introduction of electromagnetic scalar potentials and these are proven to be constant on the Killing horizons. Finally, using the relations obtained along the analysis, we generalize and simplify the recent proof for the symmetry inheritance of the 3-dimensional case, as well as give the first constraint for the higher dimensional electromagnetic fields.